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Chapter 11: Problem 10

(This problem is somewhat advanced.) Using symbols, we can write that the marginal product of labor is equal to \(\Delta Q / \Delta L .\) Marginal cost is equal to \(\Delta \mathrm{TC} / \Delta Q .\) Because fixed costs by definition don't change, marginal cost is also equal to \(\Delta \mathrm{VC} / \Delta \mathrm{Q} .\) If jill Johnson's only variable cost (VC) is labor cost, then her variable cost equals the wage multiplied by the quantity of workers hired, or \(w \mathrm{~L}\) a. If the wage Jill pays is constant, then what is \(\Delta V C\) in terms of \(w\) and \(L ?\) b. Use your answer to part (a) and the expressions given for the marginal product of labor and the marginal cost of output to find an expression for marginal cost, \(\Delta \mathrm{TC} / \Delta \mathrm{Q},\) in terms of the wage, \(w,\) and the marginal product of labor, \(\Delta Q / \Delta L\) c. Use your answer to part (b) to determine Jill's marginal cost of producing pizzas if the wage is \(\$ 750\) per week and the marginal product of labor is 150 pizzas. If the wage falls to \(\$ 600\) per week and the marginal product of labor is unchanged, what happens to Jill's marginal cost? If the wage is unchanged at \(\$ 750\) per week and the marginal product of labor rises to 250 pizzas, what happens to Jill's marginal cost?

Short Answer

Expert verified
a) \(\Delta VC = w \Delta L\) b) Marginal cost = \(w / (\Delta Q / \Delta L)\) c) If wage is $750 per week and the marginal product of labor is 150, then the marginal cost is $5 per pizza. If wage falls to $600 with unchanged marginal product of labor, the marginal costdecreases to $4 per pizza. If wage remains $750 and the marginal product of labor rises to 250 pizzas, the marginal cost falls to $3 per pizza.

Step by step solution

01

Identify Variable Cost Change

We know that the variable cost (VC) for Jill Johnson is the wage multiplied by the number of workers hired, or \(wL\). According to the problem, the wage is constant, so \( \Delta VC = w \Delta L\) .
02

Find Expression for Marginal Cost

Using the formula provided, Marginal Cost is \(\Delta TC / \Delta Q \) and also \(\Delta VC / \Delta Q\). Substituting \(\Delta VC\) from step1 formula, we get Marginal cost as \(w \Delta L / \Delta Q\). However, provided \(\Delta Q / \Delta L \) is the Marginal product, so reversing this we get \(w / (\Delta Q / \Delta L)\).
03

Find Jill's Marginal Cost

Given that the wage \(w\) is $750 per week and the marginal product of labor is 150 pizzas, substitute these values into the formula we obtained in Step 2 to derive: Marginal cost = \(750 / 150 = $5\) per pizza.
04

Evaluate the Changes

If the wage falls to $600 per week and the marginal product of labor remains unchanged, replacing these values into the formula, we get: Marginal cost = \(600 / 150 = $4\) per pizza. Hence, the marginal cost decreases. If the wage remains at $750 per week and the marginal product of labor rises to 250 pizzas, Marginal cost = \(750 / 250 = $3\) per pizza. So, an increase in the marginal product of labor leads to a decrease in the marginal cost.

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Most popular questions from this chapter

Which of the following are examples of a firm experiencing positive technological change? a. A fall in the wages JetBlue pays its mechanics leads it to lower its ticket prices. b. A training program makes a firm's workers more productive. c. An exercise program makes a firm's workers healthier and reduces the number of days the typical worker is absent. d. A firm cuts its workforce and is able to maintain its initial level of output. e. A firm rearranges the layout of its factory and finds that by using its initial set of inputs, it can produce exactly as much as before.

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